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In the aftermath of the global financial crisis, competing measures of the trend in macroeconomic variables such as U.S. real GDP have featured prominently in policy debates. A key question is whether large shocks to macroeconomic variables will have permanent effects—i.e., in econometric terms, do the data contain stochastic trends? Unobserved-components models provide a convenient way to estimate stochastic trends for time series data, with their existence typically motivated by stationarity tests that allow at most a deterministic trend under the null hypothesis. However, given the small sample sizes available for most macroeconomic variables, standard Lagrange multiplier tests of stationarity will perform poorly when the data are highly persistent. To address this problem, we propose the use of a likelihood ratio test of stationarity based directly on the unobserved-components models used in estimation of stochastic trends. We demonstrate that a bootstrap version of this test has far better small-sample properties for empirically relevant data-generating processes than bootstrap versions of the standard Lagrange multiplier tests. An application to U.S. real GDP produces stronger support for the presence of large permanent shocks using the likelihood ratio test than using the standard tests.

Does excluding food and energy prices from the Consumer Price Index (CPI) produce a measure that better captures permanent price changes? To examine this question, we decompose CPI inflation and “core” inflation into their permanent and transitory components, using a correlated unobserved-components model. The stationarity of inflation may be time-varying, so we examine the performance of the core measure of inflation separately for periods in which inflation is I(1) and I(0). For a period in which inflation appears to be I(1), we find that core inflation and the permanent component of overall inflation are closely related, but there are some caveats. For a period in which inflation appears to be I(0), we decompose the core and overall price levels and find that the permanent component of the core CPI is much more volatile than the actual core series and that the core excludes volatile permanent shocks to the overall price level.

This paper proposes a multivariate unobserved-components model to simultaneously decompose the real GDP for each of the G-7 countries into its respective trend and cycle components. In contrast to previous literature, our model allows for explicit correlation between all the contemporaneous trend and cycle shocks. We find that all the G-7 countries have highly variable stochastic permanent components for output, even once we allow for structural breaks. We also find that common restrictions on the correlations between trend and cycle shocks are rejected by the data. In particular, we find that correlations across permanent and transitory shocks are important both within and across countries.

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